In rotary fluid handling devices with radially variable working chambers, like gear pumps, vane pumps, trochoid pumps, radial piston pumps, machines or motors, for example of the type disclosed in U.S. Pat. No. 3,470,825, it was difficult heretofore to fasten the fluid handling rotary members on the driving or driven shaft of the machine, because fastening means, like keyways or splines would disturb the control face portion or cause the necessity of larger inner diameters of the control faces, which in turn would then cause greater control faces and thereby greater friction between control faces of the machine. These drawbacks restricted the efficiency of such machines and their power. One of the worst difficulties in heretofore known fluid-handling devices was that the shaft deformed under the heavy radial load and that rotary control faces were not entirely parallel to and floating adjacent the stationary control faces of the devices. This resulted in wearing and friction at certain portions of the control clearances and in high leakage at higher pressures at other portions of the control clearances on the axial ends of the fluid handling rotary members.